Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S18 / 3 / 2 / Solution

Eliminate the lower component to get $(E^2-m^2{c}^4)\phi =c^2(\sigma \cdot \Pi {)}^2\phi$. Since $[{\Pi }_x,{\Pi }_y]=ie\hslash B/c$, the Pauli identity gives $(\sigma \cdot \Pi {)}^2={\Pi }^2-e\hslash B{\sigma }_3/c$. Substitute the three momenta and rearrange:The spin-field sign follows from the charge convention and commutator, not an independent assignment.